A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

The Relationship between Physical Growth and Infant Behavioral Development in Rural Guatemala

The present study investigated the relationship between a number of anthropometric indices and behavioral development during the first 2 years of life in rural Guatemala. Length and weight were the indices most strongly correlated with behavioral development. If the effect of the infant\u27s length and weight was statistically controlled for, none of the other anthropometric variables explained a significant proportion of the variance in behavioral development. Con- trolling for length (or weight) assessed at the same age as the behavioral assessment, length (or weight) for younger ages was not significantly correlated with behavioral development. Changes in length or weight over time were correlated with changes in behavioral performance. We were unable to explain the association between physical growth and behavioral development by a number of variables including gestational age, nutrient intake, prevalence of disease, and familial characteristics

Sheldon Spectrum and the Plankton Paradox: Two Sides of the Same Coin : A trait-based plankton size-spectrum model

The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems: the biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude. While size-spectrum models have explained this phenomenon for assemblages of multicellular organisms, this paper introduces a species-resolved size-spectrum model to explain the phenomenon in unicellular plankton. A Sheldon spectrum spanning the cell-size range of unicellular plankton necessarily consists of a large number of coexisting species covering a wide range of characteristic sizes. The coexistence of many phytoplankton species feeding on a small number of resources is known as the Paradox of the Plankton. Our model resolves the paradox by showing that coexistence is facilitated by the allometric scaling of four physiological rates. Two of the allometries have empirical support, the remaining two emerge from predator-prey interactions exactly when the abundances follow a Sheldon spectrum. Our plankton model is a scale-invariant trait-based size-spectrum model: it describes the abundance of phyto- and zooplankton cells as a function of both size and species trait (the maximal size before cell division). It incorporates growth due to resource consumption and predation on smaller cells, death due to predation, and a flexible cell division process. We give analytic solutions at steady state for both the within-species size distributions and the relative abundances across species

Theoretical and experimental activities on opacities for a good interpretation of seismic stellar probes

Opacity calculations are basic ingredients of stellar modelling. They play a crucial role in the interpretation of acoustic modes detected by SoHO, COROT and KEPLER. In this review we present our activities on both theoretical and experimental sides. We show new calculations of opacity spectra and comparisons between eight groups who produce opacity spectra calculations in the domain where experiments are scheduled. Real differences are noticed with real astrophysical consequences when one extends helioseismology to cluster studies of different compositions. Two cases are considered presently: (1) the solar radiative zone and (2) the beta Cephei envelops. We describe how our experiments are performed and new preliminary results on nickel obtained in the campaign 2010 at LULI 2000 at Polytechnique.Comment: 6 pages, 4 figures, invited talk at SOHO2

Amplification of environmental fluctuations by marine ecosystems

Environmental variability is an important cause of fluctuations in marine ecosystems. Some ecosystems appear to have characteristic resonant frequencies, and even a weak environmental signal at one of these frequencies can cause large changes in population sizes. It is already known that some commercial fish stocks undergo abundance cycles which can be explained in this way, since models of their population dynamics exhibit resonances at or near the appropriate frequencies. In this paper it is shown that resonance found in Lotka-Volterra models of predator-prey systems appears to be a likely cause of many of the fluctuations found in marine ecosystems